Question

URGENTE‼️‼️

Quais as raízes da equação: log12 (x2 - X)=1 ?

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_{12}\:(x^2 - x) = 1}$

$\mathsf{log_{12}\:(x^2 - x) = log_{12}\:12}$

$\mathsf{x^2 - x = 12}$

$\mathsf{x^2 - x - 12 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-1)^2 - 4.1.(-12)}$

$\mathsf{\Delta = 1 + 48}$

$\mathsf{\Delta = 49}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{49}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{1 + 7}{2} = \dfrac{8}{2} = 4}\\\\\mathsf{x'' = \dfrac{1 - 7}{2} = -\dfrac{6}{2} = -3}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{4;-3\}}}}$